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The use of multiple representations supports and requires tasks that involve decision-making and other problem-solving skills. [2] [3] [4] The choice of which representation to use, the task of making representations given other representations, and the understanding of how changes in one representation affect others are examples of such mathematically sophisticated activities.
As in all positional number systems with an Archimedean absolute value, there are some numbers with multiple representations. Examples of such numbers are shown in the right column of the table. All of them are repeating fractions with the repetend marked by a horizontal line above it.
However, since we want to construct examples for linear representations - where groups act on vector spaces instead of on arbitrary finite sets - we have to proceed in a different way. In order to construct the permutation representation, we need a vector space V {\displaystyle V} with dim ( V ) = | X | . {\displaystyle \dim(V)=|X|.}
Representation theory studies how algebraic structures "act" on objects. A simple example is the way a polygon is transformed by its symmetries under reflections and rotations, which are all linear transformations about the center of the polygon.
In mathematics, a representation is a very general relationship that expresses similarities (or equivalences) between mathematical objects or structures.Roughly speaking, a collection Y of mathematical objects may be said to represent another collection X of objects, provided that the properties and relationships existing among the representing objects y i conform, in some consistent way, to ...
Some balanced ternary fractions have multiple representations too. For example, 1 / 6 = 0.1 𝖳 bal3 = 0.0 1 bal3 . Certainly, in the decimal and binary, we may omit the rightmost trailing infinite 0s after the radix point and gain a representations of integer or terminating fraction.
Many-valued logic (also multi-or multiple-valued logic) is a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle 's logical calculus , there were only two possible values (i.e., "true" and "false") for any proposition .
In mathematics, especially representation theory, a quiver is another name for a multidigraph; that is, a directed graph where loops and multiple arrows between two vertices are allowed. Quivers are commonly used in representation theory: a representation V of a quiver assigns a vector space V ( x ) to each vertex x of the quiver and a linear ...